l
m
x
A
B
seg AB is the intercept
In the fig.,
seg AB is the intercept formed
on transversal x by lines l and m.
n
C
INTERCEPT
=
QR
PQ
EF
FG
The ratio of the intercepts made on a transversal by three parallel
lines is equal to the ratio of the corresponding intercepts made
on any other transversal by the same parallel lines.
l
m
n
x
P
Q
R
Intercepts on x
PQ
QR
PR
y
E
F
G
Intercepts on y
EF
FG
EG
QR
PR
=
FG
EG
PQ
PR
=
EF
EG
Sol:
and EF || AB
EF || DC
AE
ED
AG
GC
=
∴
(Lines parallel to the same line are parallel to each other)
In ΔADC,
EG || DC
(As EF || DC)
∴
…(1) [By Basic Proportionality Theorem]
In ΔCAB,
CG
AG
CF
BF
=
A
B
D
C
E
F
AB || DC
Solved Example :
ABCD is a trapezium with AB || DC. E and F are points on non-parallel
sides AD and BC respectively such that EF is parallel to AB .
AE
ED
BF
FC
=
Show that
G
Join AC intersecting EF at point G
FG || AB
…(2)
∴
Sol:
AG
GC
BF
FC
=
i.e.,
[From (1) and (3)]
AE
ED
BF
FC
=
A
B
D
C
E
F
G
AE
ED
AG
GC
=
…(1)
CG
AG
CF
BF
=
…(3)
…(2)
Solved Example :
ABCD is a trapezium with AB || DC. E and F are points on non-parallel
sides AD and BC respectively such that EF is parallel to AB .
AE
ED
BF
FC
=
Show that